Bài giảng khí hậu học chương 4

G304 – Physical Meteorology and Climatology

Chapter 4
Atmospheric pressure
and wind

By Vu Thanh Hang, Department of Meteorology, HUS


4.1 The concept of pressure
• The atmosphere contains a tremendous number of gas
molecules being pulled toward Earth by the force of
gravity.
• These molecules exert a force on all surfaces with
which they are in contact, and the amount of that force
exerted per unit of surface area is pressure.
• The standard unit of pressure is the pascal (Pa).
• Air pressure at sea level is roughly 1000 mb (100 kPa)
or more precisely, 1013.2 mb.



Fig. 4-1

• The enclosed air molecules move about
continually and exert a pressure on the interior
walls of the container (a).
• Pressure can increase by increasing the
density of the molecules (b)
• Increasing the temperature (c).
• If the air in the container is a mixture of

gases, each gas exerts its own specific
amount of pressure Æ partial pressure.
• The total pressure exerted is equal to the
sum of the partial pressures Æ Dalton’s law.


4.1 The concept of pressure (cont.)
• In fact, atmospheric pressure is the mass of the air
above being pulled downward by gravity
• The pressure at any point reflects the mass of
atmosphere above that point
• The mass of atmosphere above necessarily decreases
Æ pressure must also decrease
• Air pressure is exerted equally in all directions: up,
down, and sideways


4.1 The concept of pressure (cont.)
• Surface pressure is the pressure actually observed at a
particular location, whereas sea level pressure is the pressure
that would exist if the observation point were at sea level.
• Sea level pressure allows us to compare pressure at different
locations taking into account differences in elevation.
• To correct for elevation, add 1 mb per 10 meters.
• For high-elevation sites, this method is unreliable because we
must account for compressibility of the atmosphere.


4.1 The concept of pressure (cont.)

Pressure will be less at P2 than at P1 due
to pressure decreasing with height


4.1 The concept of pressure (cont.)
• Pressure
does
not
decrease at a constant
rate.
• Surface pressure also
varies from place to place
• Horizontal
pressure
differences are very small
compared
to
vertical
differences
Fig. 4-3 Pressure decreases with altitude by
about half for each 5.5km


4.2 The equation of state
• Temperature, density and pressure are ralated to one
another
• The Equation of State (Ideal Gas Law)
p = ρRT
where p is pressure (Pa), ρ is density (kg m-3), R = 287 (J
kg-1 K-1), T is temperature (K).

• If the air density increases while temperature is held
constant, the pressure will increase, and at constant
density, an increase in temperature leads to an increase in
pressure.


Standard atmosphere: p0 = 101325 Pa, T0 = 288.15 K, ρ0 = 1.225 kg/m³


4.3 Measuring pressure
• The
standard
instrument
for
the
measurement of pressure is the mercury
barometer
• Barometric pressure is often expressed as
the height of the column of mercury in a
barometer, which at sea level averages 76
cm (29.92 in).
• To convert barometric heights to millibars:
1 cm = 13.32 mb
1 inch = 33.865 mb


4.3 Measuring pressure (cont.)
• An alternative instrument for the

observation of pressure is the aneroid

barometer (“without liquid”) which
contains a collapsible chamber from
which some of the air has been
removed.
• The weight of the atmosphere
presses on the chamber and
compresses it by an amount
proportional to the air pressure.
• Aneroid
devices
that
plot
continuous values of pressure over
extended
periods
are
called
barographs.


4.4 The distribution of pressure
• An isobar is a line that connects points having exactly
the same sea level pressure drawn at intervals of 4 mb
on surface weather maps.
• The spacing of the isobars indicates the strength of the
pressure gradient, or rate of change in pressure.
• A dense clustering of isobars indicates a steep pressure
gradient (a rapid change in pressure with distance),
while widely spaced isobars indicate a weak gradient.

A weather map showing the distribution of sea level air pressure.
The pressure is relatively low over the northeastern U.S. and
eastern Canada, and the highest and lowest pressure on the map
are only within about 4 percent of each other.


4.4 The distribution of pressure (cont.)
• If the air over one region exerts a greater pressure than
the air over an adjacent area, the higher-pressure air
will spread out toward the zone of lower pressure as
wind.
• The pressure gradient gives rise to the pressure
gradient force, which sets the air in motion.
• For pressure gradients measured at constant altitude,
we use the term horizontal pressure gradient force.
• Everything else being equal, the greater the horizontal
pressure gradient force, the greater the wind speed.


4.4 The distribution of pressure (cont.)
• The vertical pressure gradient force and the force of
gravity are normally of nearly equal value and
operate in opposite directions, a situation called
hydrostatic equilibrium.
• The Hydrostatic Equation
dp/dz = -ρg
where dp refers to a change in pressure, dz refers
to a change in altitude, and -ρg refers to density and
the acceleration of gravity

4.4 The distribution of pressure (cont.)
• Two columns of air with equal
temperatures, pressures, and
densities (a).
• Heating the column on the right
(b) causes it to expand upward.
It still contains the same amount
of mass, but it has a lower
density to compensate for its
greater height.
• Because
the
pressure
difference between the base and
top is still 500 mb, the vertical
pressure gradient is smaller.

Fig. 4-7


4.4 The distribution of pressure (cont.)
Fig. 4-8

The gradual poleward decrease in mean temperature results in denser air
occurring at high latitudes. As indicated by the hydrostatic equation, pressure
drops more rapidly with height at high latitudes and lowers the height of the
500 mb level. The dashed lines depict the height of the 500 mb level as
they would be drawn on a 500 mb weather map.

4.4 The distribution of pressure (cont.)

A 500 mb map with height contours
labeled in decameters ranging from
5880 m in the south to 5220 m in
the extreme northwest. Contours
for 500 mb maps are drawn at
60 m intervals. These maps depict
the varying heights of pressure levels.
Where height contours are close,
the pressure gradient force is large.

Fig. 4-9


4.5 Forces affecting the speed and direction
of the wind
• The unequal distribution of air across the globe establishes
the horizontal pressure gradients Æ movement of air as wind
• If no other force Æ the wind always flow in the direction of
pressure gradient force
• The pressure gradient force sets air in motion from higher
pressure to lower pressure
• Two other forces:
- due to planetary rotation Æ coriolis force Æ alters the
direction of the wind
- friction force Æ slows the wind

4.5 Forces affecting the speed and direction
of the wind (cont.)
• The pressure gradient force (PGF):
•

Horizontal pressure gradient force per unit
mass:

1 dP
PGF =
ρ dn
•

ρ = air density (1.2 kgm-3 at sea level)

•

dP/dn = horizontal gradient of pressure (SI
units)
– mb/km Æ Pa/m
– 1mb = 100Pa; 1km = 1000m


4.5 Forces affecting the speed and direction
of the wind (cont.)
• The coriolis force (CF):
• Deflective force (per unit mass):
CF = 2ωVsinφ
• ω = angular velocity of spin (Earth: 2π/24 rad/hr = 7.29*10-5

rad/s)
• V = velocity of mass (wind speed)
• φ = latitude
• Coriolis parameter f = 2ωsinφ


4.5 Forces affecting the speed and direction
of the wind (cont.)
• The coriolis force (CF):
•

Æ magnitude
proportional to:

of

deflection

directly

– Horizontal velocity
– Sine of latitude
•

Æ effect is maximum at poles and zero at
equator

•

deflection (turning) of the wind to the right

in the NH and to the left in the SH

•

acting on any moving object, increases
with the object’s speed

•

changes only the direction of a moving
object, never its speed


4.5 Forces affecting the speed and direction
of the wind (cont.)
• Geostrophic balance:
• In absence of friction (from surface)
OR centripetal forces (arises from
curve-isobars)
• ONLY two equal & opposite forces
acting on an air parcel
• For steady flow:
1 dP
−
= 2ωV sin φ
ρ dn
• PGF = CF Æ Geostrophic wind

VG = −

1
dP
2ω sin φρ dn

In geostrophic balance air flows parallel to isobars with high
pressure to the right in NH


4.5 Forces affecting the speed and direction
of the wind (cont.)
• The friction force (FrF):
•

Winds are slowed down by roughness of the surface over which it flows
Æ friction

• Friction: V ↓, CF ↓ Æ Imbalance & cross-isobaric flow

• Friction is important within the lowest 1.5 km of the atmosphere
(planetary boundary layer - PBL)